The timing and location of the initiation of convection is the one of the fundamental issues in precipitation and severe storm forecasting. Much recent observation and numerical simulations show that the convection initiation is general associate with the leading edge of meso-scale system, e.g. seebreeze and dryline. In some special case the colliding frontal boundary could induce more intensity convection, however the dynamic process is inadequately understood. A simplified two-dimensional non-hydrostatic model was used to investigate theoretically the dynamics of the frontal boundary collision and associated with convective initiation. The fluid variables are expanded as power series in time. The first and second order solution could describe the gross features of frontal boundary collision. Comparison with the alone frontal boundary case, the horizontal convergence and vertical velocity are enhanced when the leading edge of front are collided. The colliding process in the different stratified cases is also discussed.